Apparatus for determining earthwork volumes

ABSTRACT

Measuring and calculating apparatus with which engineering functions necessary to the designing layout and construction of structures such as roads, canals, etc., can be performed easily and accurately directly from a contour map of the area in which the structure is to be constructed, thereby eliminating the need for extensive on-site observations or time consuming template utilization.

United States Patent 1191 Raneses 4s 1 July 17, 1973 APPARATUS FORDETERMINING 2,975,521 3/1961 Holmes 33/75 R EARTHWORK VOLUMES [76]Inventor: Pedro c. Raneses. 1085 California Primary Examiner-StephenTomsky Ave Salt L k Cit U h Attorney-B. Deon Criddle [22] Filed: Jan.25, 1971 21 Appl. No.: 109,146 [571 ABSTRACT Measuring and calculatingapparatus with which engi- 52 us. (:1 33/121, 33/1 v 235 88 "eefingfunctiqnsnecessary the designing laymtmd 51 1111. c1. G066 3/00, Gdlb5/26 nstrucfi0n of Struflures such as roads, canals, etc., [58] Field atSearch 33/1 v 1 SB 1 R can be Perfmmed easily and accurately directly mma 3 235/78 88 contour map of the area in which the structure is to beconstructed, thereby eliminating the need for extensive [56] ReferencesCited on-site observations or time consuming template utili- UNITEDSTATES PATENTS 2,972,810 2/1961 Davis 33/121 5 Claims, 6 Drawing Figuresu we 50.. mm c 600-100 1 an PAIENIEB -3.745.658

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ATTORNEY PATENIEDJUL 1 H913 sum 3 M3 FIG 6 INVENTOR: PEDRO C. RANESESATTORNF Y APPARATUS FOR DETERMINING EARTHWORK VOLUMES BRIEF DESCRIPTIONOF THE INVENTION 1. Field of the Invention This invention relates tomeasuring and calculating apparatus for performing engineering functionsin connection with the layout and design necessary to construction ofroads, canals, etc. While the engineering structure described herein inconnection with the apparatus of the invention is a road it will beobvious that the same apparatus can be used in the design andconstruction of other similar constructions.

2. Prior Art Modern road construction has developed in many areas inrecent years. Formerly, roads were constructed to closely conform to theexisting terrain and cut and fill operations were held to a minimum,This was satisfactory, so long as vehicles did not travel too fast andso long as the number of vehicles using them was not too great. Roads soconstructed often produced a roller coaster effect on vehicles travelingover them and with the development of faster vehicles, and the greatincrease in the number of automobiles such roads were no longersatisfactory. It is now well recognized that modern highway constructionrequires a road with smooth surfaces and gentle horizontal and verticalcurves. This means that extensive excavation and filling is oftennecessary to provide a smooth roadbed. Inasmuch as the expenses ofconstruction are to a large extent directly related to the costs ofexcavating and the hauling and compacting of fill materials, it ishighly desirable to construct a road such that a minimum amount ofmaterial must be moved and to make the haul lengths for that movement asshort as possible.

The present invention provides an apparatus with which cut and fillvolumes can be easily computed to offset each other, to the extentpossible, by enabling an operator of the apparatus to calculate slopestake locations and to compute the effect of such locations as to filland cut requirements from a contour map.

While some calculating devices have been available in the past for usein plotting a highway location, none have enabled an operator, 'usingmerely such apparatus and a contour map, to easily locate theintersection of the ground with that of a proposed side slope of theroad and, based on that intercept point, to compute the volume of earthto be removed or needed to fill to achieve the desired construction.Instead, in the past, it has been necessary to plot cross-sectionalareas at selected intervals along the road centerline prior to thecomputation of earthwork volumes. Such plottings frequently requireactual on the job surveys and if a centerline is subsequently relocated,because of a terrain obstacle, for example, the plottings must berepeated. Since the cross-section plottings are taken at set stationsalong the road centerline radical terrain changes between the stationsmay not be considered in making the volume calculations.

SUMMARY OF THE INVENTION Principal objects of the present invention areto provide apparatus for utilization with a contour map in determiningintercept points between the ground and a road, or other such structure,side slope and in determining the volumes of material to be cut and tobe filled incident to construction of the structure.

Another object is to provide such an apparatus that can also be used toquickly and easily properly position culverts, ditches and other suchdrainage structures necessary to proper construction of the structure tobe built.

Principal features of the present invention include an indicator and acalculator, each of which is separately useful for various functions butthat are used together to perform the total engineering functions setforth in the foregoing objects.

The indicator is used to locate intercept points of the ground and theside slope, thereby enabling computation, utilizing the calculator andwithout plotting, of either the amount of material needed to fill asection between stations to the desired roadbed level or the amount ofmaterial needed to be cut to produce a road bed at the desired elevationand with the required side slopes.

The slope intercept point indicator consists of a series of radiatingscales, each having a slot therein to receive a sliding bar. The bar hasa pair of pointers mounted to slide therealong. A number of radiatingscales are used to make up a complete set, with each having an indice onit expressing the relationship between gradations on the radiatingscales and gradations on the associated sliding bar. Thus, therelationship may be any ratio between %:l and 10:1, to encompass themost common side slope ratios used. Obviously, however, other scalescould as well be used in conjunction with other side slope ratios,should these be desired. The slope to be utilized, i.e. 2:1, 4:1, etc.,is determined by the height differential between the road and the slopeintercept point and the proper ratio is therefore determined by thepoint of intercept. Accordingly, several radiating scales may have to betried before the proper one is determined. The indices on the radiatingscales and sliding bar are scribed thereon in accordance with the scaleof the contour map which is to be used. Generally, in highwayconstruction operations, a map scale of feet or 100 feet on the groundto a 1 inch map distance is used. Therefore, the indices on theradiating scales and sliding bar are preferably scribed in sets so as toprovide for a utilization of the same radiating scale with either a 50foot to 1 inch or foot to 1 inch contour map. Either map can then beused, with different indices of the radiating scales and sliding barbeing utilized as necessary.

As previously noted, the sliding bar has a pair of pointers mounted totravel on it. One such pointer may be utilized to transfer a proposedhighway width from the sliding bar to a map starting reference point andthe other pointer may be used to locate the point of intersectionbetween an indice on the radiating scale with an actual map contour,which intersection establishes the slope intercept point.

Additional features include scales on the individual radiating scaleswhich are used to compute either cut or fill. Folding scales areprovided and have a zero beginning point located so as to facilitatecomputations. Means are provided to lock the sliding bar to theindividual radiating scale when their proper relative positions areachieved.

The slope point indicator is used to locate an intercept point on acontour map, i.e. a point where the highway side slope intersects thenormal terrain. The contour map used reflects elevations, so thedifference in elevation between the intercept point and the highwayshoulder at any station along the road is readily ascertainable, withthe slope point indicator positioned so as to locate the interceptpoint. The indice markings between the side slope intersection and theroadbed correspond to elevations along the proposed slope line. Thedifference in elevation between the side slope elevation, as readdirectly from the slope point indicator, and the actual ground asindicated by the contours of the contour map, are readily determined.

The calculator is utilized to compute a running total of the variousheight differentials for a given section. Preferably, the calculator hastwo wheels axially connected to rotate independently of one another anda pointer, also connected so as to rotate about the axle. Scales arescribed on the wheels such that they can be used to input the elevationdifferentials, which are added or subtracted in the computer to give atotal plus (fill) or minus (cut) of the height differentialsincrementally determined along the base. The pointer may be arranged toturn an indicator located in the face of the top wheel so that each timethe zero indice is passed on the scale, each zero passed representing100 feet of height differential, one digit, in either a positive or anegative direction, depending upon whether the 100 foot of heightdifferential represents cut or fill is changed with respect to theindicator. Utilizing two other scales scribed on each wheel, whichscales correspond to the C and D scales of a standard slide-rule, thetotal net height differential can be multiplied by the increment ofdistance selected i.e. 5 or feet, for example, to thereby determine theaccumulated cross sectional area above or below the base line. Todetermine earthwork volume the distance between bases at adjacentstations along the road is multiplied by the cross sectional areacomputed, again using the C and D scales of the calculator, to therebyobtain the volume in cubic feet of material to be filled or cut. Thevolume thus obtained comprise the volume of cut or fill materialnecessary to construction of the highway side slope between stationsalong the road. The volume of cut or fill material necessary toconstruction of the highway roadbed itself is calculated by determiningthe differential elevation between the desired highway elevation and theground elevation, multiplied by the width of the bed and the distancebetween stations along the road. The calculator is used to determine thesummation of height differentials and the C and D scales are used tomultiply the calculated total height differentials by the length betweenstations, to determine the earthwork volume necessary to adjacentstations.

The combined use of the indicator and calculator apparatus enables userto determine side slope locations and earthwork volumes without the useof extensive profile drawings or the need for on-site observations. Aswill be apparent the apparatus can be used with contour maps having anyscale if the scale distances on the radiating scales and sliding bar arearranged to reflect the map scale.

Further objects and features of the invention will become apparent fromthe following detailed description, taken together with the accompanyingdrawings.

THE DRAWINGS FIG. 1 is a top plan view of the cross sectional areacalculator;

FIG. 2, a side view of the cross sectional area calculator taken on line2--2;

FIG. 3, a side view of a segment of the cross sectional area calculatortaken on line 3-3;

FIG. 4, a top plan view of the slope intercept calculator;

FIG. 5, a schematic view showing the drive assembly for the indicator ofthe calculator; and

FIG. 6, composite contour map section with proposed highway centerlinethereon and a typical cross sectional profile.

DETAILED DESCRIPTION Referring now to the drawings:

The cross sectional area calculator 10 consists of two wheels 11 and 12.Wheel 11 has the largest diameter and is fastened beneath wheel 12. Thetwo wheels surround a common central post 13 and are held in place by ascrew 14 threaded into one end of post 13. An indicator arm 15 is alsoheld in place on the center post 13 by screw 14. A calculator base 16 isalso provided and is secured to center post 13 by a screw 17 threadedinto the other end of the post. While not always necessary an indicator18, FIGS. 1 and 2, is preferably incorporated in the calculator and isconnected to the indicator arm 15 such that as the arm is turned past azero marking on a scale B of wheel 12, to thereby reflect feet indifferential elevation, the indicator l8 registers a 1, and so forth.The gearing for this relationship of the indicator arm 15 to indicator18 is shown schematically in FIG. 2 and consists of a gear train havingtwo gears 18a and 18b. Gear 18a is turned by the indicator arm 15 and asit rotates it turns the gear 18b which is formed around the indicator18.

Wheel 11 has inner and outer scales C and A, respectively, scribedthereon and wheel 12 has inner and outer scales D and B scribed thereon.Scales A and B are reflections of one another and are arranged to beadjacent. Scales C and D, while separated by scales A and B are alsoreflections of one another.

In operation of the calculator to determine transverse cross sectionalareas at stations along a roadway, for example, the A and B scales areutilized to determine a cumulative vertical height between the actualground elevation and the proposed slope line at predetermined horizontalincrement points spaced, for example, 5 feet apart. This cumulativeheight is calculated by setting the hairline indicator 15a on indicatorarm 15 over the zero on scale A and rotating both scale A and indicatorarm 15 together until the hairline indicator is aligned with a number onscale B representative of the ground elevation. Scales A and B areimmobilized and indicator 15 is rotated to align the hairline indicatorwith the height of the proposed slope elevation on scale B. Scale A isreleased from scale B and, with indicator 15 held to scale A, is rotateduntil the hairline indicator 15a is aligned with the next groundelevation, as read on scale B. Scales A and B are again held togetherand the hairline indicator 15a is rotated until it is aligned with theheight of the proposed slope line at the next increment point, as readon scale B. The procedure of unlocking scales A and B and rotation ofhairline indicator 15a is then repeated at each predetermined selectedincrement point with the final reading on scale A reflecting thecumulative positive or negative height differential of the proposedslope to the ground at the selected increments. The cross sectional areais then determined by a multiplication of the cumulative height by thepredetermined increment of distance, which in the example given is fivefeet. These multiplication functions are easily accomplished asconventional slide-rule operations merely by utilizing the C and Dscales of the present invention. To multiply with the scales, indicatorhairline a is rotated until it is in alignment with the number I onscale D. The indicator hairline 15a and the number 1 on scale D are thenrotated until they are in alignment with the number on scale C which isto be multiplied. Scales C and D are then immobilized and the indicatorhairline is rotated until it is aligned with the multiplier on scale D.The answer is then read under the hairline from scale C. Successivemultiplications can be accomplished by relocating the indicator l5 andthe number 1 on scale D to be in alignment with said resultant on scaleC and thereafter rotating the indicator to a new multiplier on scale Dbefore reading the new answer on scale C.

Example 1 Utilizing the contour map and highway side slope profile shownin FIG. 6, the cross sectional area of fill in this embodiment iscalculated from a determination of the slope intercept point X. Thispoint is determined utilizing the slope intercept point indicator aswill be hereinafter described in detail. The proposed highway side slopeis then drawn from the point Y, which is located at the edge of theproposed highway and therefore has a predetermined proposed elevation,to point X. The difference in elevation between the slope interceptpoint X and the highway edge Y is then readily determined from thecontours and the corresponding indice on the slope point indicator to be18 feet and the horizontal distance between these two points is sealedoff and is found to be 25 feet. The indices of the slope point indicatorwhen it is positioned so as to locate the slope intercept between thehighway shoulder and the intercept point reflect the elevations of theproposed slope. Therefore by determining what increment of distance isto be used, by a direct reading of the contour map and the positionedscale at that point, the proposed slope elevation and the actual groundelevation can be determined without additional calculations or readings.The slope line elevation minus the ground elevation beneath eachincrement point gives the depth of the fill required at that incrementpoint.

The desired cross sectional area is determined by setting indicatorhairline l5a over the zero reading on scale A, holding the alignedindicator l5 and scale A together while turning them until the hairlineis aligned with the ground elevation, i.e. 20, on scale B. Scales A andB are then held together and the indicator hairline 15a is rotated untilit is aligned with the highway elevation, i.e. 30, on scale B. Scale Ais released from scale B and the indicator 15 is held with respect toscale A and is rotated until the hairline 15a is over the groundelevation, i.e. 18, at the first five foot increment on scale B. ScalesA and B are again held together and indicator 15 is rotated to place thehairline 150 over the elevation of the side slope, i.e. 26%, at thefirst five foot increment on scale B. This procedure is cumulativelyfollowed at each 5 foot increment point until point X is reached atwhich point the side slope intersects the ground. Scale A reflects thetotal cumulative combined height difierential between the ground and theproposed side slope as obtained at the increment points, i.e. 33.0 feet,in this example. Using the C and D scales, this differential 33.0 feetis multiplied by the increments of distance (5 feet) to derive the totalcross sectional area (I65 ft?) between the slope line and ground.

By adding together adjacent areas calculated as above described anddividing this sum by two to obtain an average and thereafter multiplyingthe result by the distance between the areas, the volume of earth to beremoved or filled along the segment of road calculated can be readilydetermined.

Theslope intercept point indicator 20 includes a radiating scale 21which has indices commencing at zero points 21a, 21b, 21c, and 21d thatcontinue in increments of ten and which indices are scribed thereoncorresponding to scale distances on contour maps used therewith inhighway planning. The distances between the indices, shown scribed alongthe sides of the scale 21 in FIG. 4, reflect the map scale of a highwayplanning type contour map such as the map shown in FIG. 6. Such contourmaps usually incorporate scale relationships of 50 or feet on the groundas equal to an inch on the contour map. Therefore, an inch on theradiating scale 21 or on a sliding scale 25 of the invention willnormally reflect a ground distance of either 50 or 100 feet, dependingupon the contour map intended for use. FIG. 4 shows an enlarged top planview of the radiating and sliding scales 21 and 25 making up the slopeintercept point indicator 20 of the present invention. As shown therein,the radiating scale 21 indices are identified at increments of 10 by aplurality of reference numerals. The different numbers aligned withparticular scale indices markings represent scales commencing atdifferent starting, or zero points 21a, 21b, and 21c respectively, thatcontinue through 100 along the radiating scale 21, forming what arecommonly known as folded scales. An operator can select a mostconvenient folded scale for use, as will be discussed later herein, inlocating a slope intercept point on the particular contour map. Commonlythe indices will correspond to the distances of maps having a mapdistance of one inch equal to either 50 or 100 feet on the ground, thesebeing the ground-map distance ratios most commonly used for highwaydesign work. As shown in FIG. 4, from the indices markings zero points21d and 21c. Each of the indices extends in increments of ten to points2le and 21f, respectively, that have assigned values of 90. The indiceson the radiating scale 21 are laid out on opposite edges of the scale torepresent cut or fill requirements. Thus, the indices shown generally at22 are applicable for out determinations and the indices shown generallyat 23 are applicable for fill determinations. Each radiating scale 21represents a ratio of horizontal versus height (i.e. 10:1 to xfizl) asmarked adjacent to the indices. The ratio requirement used in anyinstance is determined by the amount of cut or fill required toconstruct the highway in accordance with government established highwaydesign criteria. A complete set of radiating scales 21 will provide ascale for any possible established ratio.

Each radiating scale 21 has a sliding bar 25 in the center thereofarranged to reciprocate longitudinally. The sliding bar 25 has indices25a numbered from zero to 600 scribed thereon representing to a grounddistance corresponding to the scale of the particular contour map beingused. Thus, the map ratios, i.e. 50 foot to 1 inch of ground distance tomap distance, are represented by the indices on the sliding bar 25.

Sliding scale 25 reciprocates freely within a central channel 26 of theradiating scale 21, and can be locked to the radiating scale by turninga set screw 27, which acts to bind the sliding scale 25 within channel26.

Moving across sliding scale 25 and traveling within grooves 28a and 28bformed in the sides of said scale, are two slide pointers 29 and 30. Thepointers 29 and 30 each incorporate pointed ends 29a and 30 arespectively that extend therefrom to travel over the indices on eachside of the radiating scale 21 as the pointers travel in grooves 28aand28b. The pointers are used to locate points on a contour map withrespect to relative settings of the radiating and slide scales.

To operate the slope intercept point indicator for the purpose ofdetermining intercept points between the actual ground and proposedhighway slope, pointer 29 is first set at the zero indice mark on thesliding scale 25. Pointer 30 is then set at a point on the sliding scale25 corresponding to the width of the proposed highway, from its controlline to its shoulder. Sliding scale 25, having the pointers 29 and 30 sopositioned is then moved within groove 26 until pointer 30 is opposite apoint on radiating scale 21 corresponding to the last two digits of theelevation of the highway shoulder at a station where the side slope isto be determined. Scales 21 and 25 are then clamped in their relativepositions. The clamped scales 21 and 25 are then positioned on thecontour map being used such that the pointer 29, which is positioned atzero on sliding scale 25, is on the highway control line with thepointer 30 indicating the shoulder or station from where the side slopeis being determined. The clamped scales are then unclamped and theslding scale 25 is made to slide in groove 26 in scale 21 and withinpointer 30 until the edge of pointer 29 butts thereagainst, whereat thescales are again clamped together and are made to extend normal to thehighway. Pointer 29 is thereby positioned on the located shoulder andindicates on scale 21 the height of said shoulder. From an examinationof the roadway elevation and the proximate contours, it is possible todetermine whether the cut 22, or fill 23, indices arranged along theopposite edges of the radiating scale 21 should be used, which cut andfill indices 22 and 23 have the same equivalent relationship to thescale of a contour map, such as the contour map of FIG. 6, but whichindices are numbered oppositely to one another. An inspection is thenundertaken of radiating scale 21 to find the location at which an indicemarker intersects one of the map contours. Some interpolation may berequired as the contours and indices of the radiating scale 21 arenormally marked in two foot increments, but accuracy should be possibleto within one foot. After the intersection is located pointer 30 ismoved thereto to identify the intersection until the map can beappropriately marked.

Example 2- Utilizing the contour map of FIG. 6, the slope interceptpoint indicator is used to locate slope intercept point X. Highwayconstruction standards dictate the ratio of horizontal distance toheight for various slopes. Therefor, based on experience and the natureof the terrain, the operator will first select the radiating scalehaving the ratio (2.1, 4.1, etc.) that he believes will fit-the existingconditions. If his selection is in error he will have to select anotherindicator and recompute the slope intercept point. To locate point Xusing the radiating scale selected, pointer 29 is positioned over thezero reading on sliding scale 25 and pointer 30 is moved to a point onsliding scale 25 refleeting the highway width from a control line, i.e.30

feet. So aligned, the sliding scale with pointers positioned thereon ismoved within groove 26 in radiating scale 21 until pointer 30 isopposite to the last two digits of the elevation of the highway shoulderfrom where the proposed highway slope is to be constructed (coincidently30 in this example). Scales 21 and 25 are then clamped together in theirrelative positions by set screw 27. The terrain over which the proposedroadbed is travelled is evaluated, by inspecting the contour map, todetermine whether the proposed roadbed, having a known predeterminedelevation at any point will be above the ground, thereby requiring fillfor the side slope or below the ground so that cutting of the side slopewill be required. In the example given, the proposed roadbed is abovethe ground and fill is therefor required. Accordingly, an appropriatefill indice on the radiating scale 21 is used.

Scales 21 and 25, that locked together, are placed on the contour map ofFIG. 6 and are positioned such that pointer 30, arranged on scale 21 toindicate numeral 30 to be the last two digits of the proposed shoulderelevator of 6030 feet, is positioned on the control line, extendingnormal thereto, with pointer 30, resting at a point representing 30 feeton scale 25, indicates on the map the location of the highway shouldershown herein as point Y and pointer 29, is spaced apart from pointer 30,and rests on a zero indices marking on scale 25. After the map isappropriately marked the scales 21 and 25 are released and scale 25 ismade to slide within pointer 30 that is held stationary to scale 21 andin groove 26 in radiating scale 21 until pointer 29 butts againstpointer 30, whereat the scales are again clamped together. Pointer 29,aligned with zero on scale 25, is thereby positioned above point Y,allowing pointer 30 to be moved therefrom to be used in locating thescale 21 and the contour map intercept point. Point Y is representativeof any point on the edge of the road from which a slope line is toextend. The scales 21 and 25 are positioned to extend transverse to theproposed highway centerline. A point of intersection of the radiatingscale 21 with a contour on the contour map is sought i.e. where there isa junction of a point on the radiating scale 21 reflecting a heightcrosses a corresponding contour also reflecting height (in this examplepoint X is at 12 or 6012). Pointer 30 is moved to this intersection orjunction to reflects the slope intercept point of the proposed slopewith the ground. Once located, the height differential between theintersection and the proposed highway is determined. This differentialis checked to see if the proper ratio, 2:1, 4:1, etc., was used as perhighway construction standards. If an incorrect scale was used, anotherscale must be selected and the process repeated. If the selection wascorrect, the actual slope intercept point has been obtained and theindices on the slope point indicator between the setting for point Y andthe junction with the ground X indicate the elevations of the proposedside slope above the ground. Volumes of material can therefore becalculated using the process of Example 1.

Once the intercept point has been determined, it can be used tocalculate areas and volumes as heretofore described using the crosssectional area calculator.

The entire process of point interception and volume calculation can beaccomplished using the outlined apparatus and acontour map. Obstructionscan be recognized and planned for by relocation or adjustment of theheight of the roadbed. Using the apparatus herein described, a largeamount of highway planning can be accurately and quickly accomplished inan office and many of the time consuming and expensive on-siteobservations heretofore required can be eliminated.

Although a preferred form of the apparatus of my invention and apreferred method of its use has been herein disclosed, it is to beunderstood that the present disclosure is by way of example and thatvariations of both the apparatus and method are possible withoutdeparting from the subject matter coming within the scope of thefollowing claims which subject matter I regard as my invention.

1 claim:

1. A slope intercept point indicator comprising a radiating scale havingindices scribed thereon that represent increments of heightcorresponding to the scale of a contour map, and that are calculated inaccordance with a designated side slope ratio;

a bar scale having indices scribed thereon that conform to the scale ofa contour map;

means for releasably connecting said bar and said radiating scaletogether at variable relative positions, whereby the alignment ofindices of the two scales are maintained; and

at least one pointer, movable with respect to the bar scale andradiating scale whereby indices marks representing distance can belocated, identified and accurately transferred to the contour map andwith which indicator the intersection between a point on a contour mapand a corresponding indices marking can be identified.

2. A slope intercept point indicator as in claim 1, wherein theradiating scale has indices representing fill on one side thereof andindices representing cut on the other and has folded scale type indiceswhereby multiple zero points are available from which to computedistance therewith.

3. A slope intercept point indicator as in claim 1, wherein theradiating scale has a groove running the length thereof; and the barscale is arranged to slide freely in said groove.

4. A slope intercept point indicator as in claim 3, wherein the lockingmeans consists of a hand-operated screw threaded through the bar scalewith its head resting against the radiating scale which screw, whenproperly turned, causes a binding force to be applied between theradiating scale and the bar scale thereby securing the two scalestogether.

5. A slope intercept point indicator as in claim 1, wherein two pointersare slidably attached to the bar and radiating scale, and travel alongsaid bar scale, each pointer having pointed ends projecting from eachside thereof, and said pointers being arranged to travel along theindices of the radiating scale, whereby they can be used to align saidradiating scale indices and bar scale indices with contour map points.

1. A slope intercept point indicator comprising a radiating scale havingindices scribed thereon that represent increments of heightcorresponding to the scale of a contour map, and that are calculated inaccordance with a designated side slope ratio; a bar scale havingindices scribed thereon that conform to the scale of a contour map;means for releasably connecting said bar and said radiating scaletogether at variable relative positions, whereby the alignment ofindices of the two scales are maintained; and at least one pointer,movable with respect to the bar scale and radiating scale wherebyindices marks representing distance can be located, identified andaccurately transferred to the contour map and with which indicator theintersection between a point on a contour map and a correspondingindices marking can be identified.
 2. A slope intercept point indicatoras in claim 1, wherein the radiating scale has indices representing fillon one side thereof and indices representing cut on the other and hasfolded scale type indices whereby multiple zero points are availablefrom which to compute distance therewith.
 3. A slope intercept pointindicator as in claim 1, wherein the radiating scale has a grooverunning the length thereof; and the bar scale is arranged to slidefreely in said groove.
 4. A slope intercept point indicator as in claim3, wherein the locking means consists of a hand-operated screw threadedthrough the bar scale with its head resting against the radiating scalewhich screw, when properly turned, causes a binding force to be appliedbetween the radiating scale and the bar scale thereby securing the twoscales together.
 5. A slope intercept point indicator as in claim 1,wherein two pointers are slidably attached to the bar and radiatingscale, and travel along said bar scale, each pointer having pointed endsprojecting from each side thereof, and said pointers being arranged totravel along tHe indices of the radiating scale, whereby they can beused to align said radiating scale indices and bar scale indices withcontour map points.